Hello, I am writing in response to your question.
From your description, it's clear that you're angry because your half-sister wanted an iPad and your mother gave her one instead of doing what you wanted. This may not be the whole story, so what emotions are really behind this anger?
I understand your feelings. It's clear you prioritize your half-sister. You may not get along, and you may disapprove of some of her actions. It's understandable you feel angry.
This situation must be handled.
(1) Learn to recognize your emotions.
Everyone has emotions, but what is behind them? You may not yet be able to feel why you are angry, so you may have such emotions, doubts, etc. When emotions arise, you must avoid being controlled by them. Understand and be aware of your emotions, and manage them well. You can handle your emotions yourself.
(2) Your mother is too indulgent with your younger sister. That's why you're feeling this way.
Your mother unconditionally dotes on your younger sister, and your sister's actions make you feel that you are still immature and love to play. You feel unfairly treated by your mother's actions and are angry about it.
(3) Your mother's treatment of your younger sister makes you feel unfairly treated.
You're emphasizing that this is your half-sister and that you're fighting for your mother's love. It's clear you feel your mother favors your sister, which naturally leads to jealousy and dissatisfaction. This is likely a contributing factor.
You must learn to manage and control your emotions, regardless of what they may be. The way parents treat others is out of our control. The only thing we can do is take care of our own affairs, learn to be independent and grow up, learn to care for ourselves and be responsible for ourselves.


Comments
I can totally relate to your concerns. It's a tricky situation because you want to support her education but also worry about how much screen time she already has. Seems like setting boundaries and goals for her to earn the iPad could have been a good approach.
It sounds frustrating that despite your careful planning, your sister found out anyway. Now it seems like the excitement has taken over and all she can think about is getting her hands on it. Maybe redirecting her focus back to her studies would help ease the tension.
Your intention was noble, trying to balance reward with responsibility. But once kids get wind of a new gadget, they can't think of anything else. Perhaps engaging her in different activities might take her mind off the iPad for a while.
It's clear you're trying to do what's best for her longterm. Kids these days are so techsavvy; it's almost impossible to keep secrets from them. Involving her in the decisionmaking process might help her appreciate the value of the iPad more as a tool rather than just a toy.
You're right to be cautious about giving in too easily. It's important for her to learn that rewards come from effort. Maybe this could turn into a learning opportunity about patience and delayed gratification, even if it's challenging in the moment.